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            <p>这篇博客主要是整理看过的有关Massive MIMO的论文，英文为主，做一下简单的名录和链接整理，便于以后查找和写论文引用。</p>
<a id="more"></a>

<h1 id="Part-1-Survey-amp-Tutorial"><a href="#Part-1-Survey-amp-Tutorial" class="headerlink" title="Part 1 Survey &amp; Tutorial"></a>Part 1 Survey &amp; Tutorial</h1><h2 id="1-1Massive-MIMO-Detection-Techniques-A-Survey"><a href="#1-1Massive-MIMO-Detection-Techniques-A-Survey" class="headerlink" title="1.1Massive MIMO Detection Techniques: A Survey"></a><a href="http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=8804165&isnumber=5451756" target="_blank" rel="noopener">1.1Massive MIMO Detection Techniques: A Survey</a></h2><p><strong>(这是我看过的对线性大规模检测最为全面的Survey之一，初入门者可以看，也可以作为论文查找目录)</strong></p>
<p><strong>Citation</strong>: M. A. Albreem, M. Juntti and S. Shahabuddin, “Massive MIMO Detection Techniques: A Survey,” in <em>IEEE Communications Surveys &amp; Tutorials</em>. doi: 10.1109/COMST.2019.2935810 </p>
<h2 id="1-2-Massive-MIMO-An-Introduction"><a href="#1-2-Massive-MIMO-An-Introduction" class="headerlink" title="1.2 Massive MIMO: An Introduction"></a>1.2 <a href="http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=7064850&isnumber=7056593" target="_blank" rel="noopener">Massive MIMO: An Introduction</a></h2><p><strong>(这篇主要是介绍整体MIMO系统，不专注与任何一个单独的流程)</strong></p>
<p><strong>Citation</strong>: T. L. Marzetta, “Massive MIMO: An Introduction,” in <em>Bell Labs Technical Journal</em>, vol. 20, pp. 11-22, 2015. doi: 10.15325/BLTJ.2015.2407793 </p>
<h2 id="1-3-Fifty-Years-of-MIMO-Detection-The-Road-to-Large-Scale-MIMOs"><a href="#1-3-Fifty-Years-of-MIMO-Detection-The-Road-to-Large-Scale-MIMOs" class="headerlink" title="1.3 Fifty Years of MIMO Detection: The Road to Large-Scale MIMOs"></a>1.3 <a href="http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=7244171&isnumber=7331734" target="_blank" rel="noopener">Fifty Years of MIMO Detection: The Road to Large-Scale MIMOs</a></h2><p><strong>(非常全面的MIMO检测入门综述，主要注重明确MIMO检测算法的发展和检测过程中影响性能的主要关键因素)</strong></p>
<p><strong>Citation</strong>: S. Yang and L. Hanzo, “Fifty Years of MIMO Detection: The Road to Large-Scale MIMOs,” in <em>IEEE Communications Surveys &amp; Tutorials</em>, vol. 17, no. 4, pp. 1941-1988, Fourthquarter 2015. doi: 10.1109/COMST.2015.2475242 </p>
<h1 id="Part-2-Dissertation-Doctoral-or-Master’s"><a href="#Part-2-Dissertation-Doctoral-or-Master’s" class="headerlink" title="Part 2 Dissertation (Doctoral or Master’s)"></a>Part 2 Dissertation (Doctoral or Master’s)</h1><h2 id="2-1-Bei-Yin-Low-Complexity-Detection-and-Precoding-for-Massive-MIMO-Systems-Algorithm-Architectures-and-Application"><a href="#2-1-Bei-Yin-Low-Complexity-Detection-and-Precoding-for-Massive-MIMO-Systems-Algorithm-Architectures-and-Application" class="headerlink" title="2.1 Bei Yin - Low Complexity Detection and Precoding for Massive MIMO Systems: Algorithm, Architectures, and Application"></a>2.1 Bei Yin - Low Complexity Detection and Precoding for Massive MIMO Systems: Algorithm, Architectures, and Application</h2><p><strong>(B.Yin 的博士论文是比较全面的讲述NS和CG两种近似矩阵求逆算法的文章，这两大章节的叙述顺序与细节格式值得参考学习)</strong></p>
<p><strong>主要内容：</strong></p>
<ul>
<li><p>NS（纽曼级数展开法）</p>
<ul>
<li>NS展开数学公式推导</li>
<li>NS的LLR数学推导</li>
<li>FPGA实现</li>
<li>ASIC实现</li>
</ul>
</li>
<li><p>CG（这里的CG包含传统CG和CGLS）</p>
<ul>
<li>CG迭代公式推导</li>
<li>CG优化成CGLS</li>
<li>CG和CGLS的伪代码</li>
<li>CG的ASIC实现细节硬件结构</li>
</ul>
</li>
</ul>
<h2 id="2-2-Christoph-Studer-Interative-MIMO-Decoding-Algorithms-and-VLSI-Implementation-Aspects"><a href="#2-2-Christoph-Studer-Interative-MIMO-Decoding-Algorithms-and-VLSI-Implementation-Aspects" class="headerlink" title="2.2 Christoph Studer - Interative MIMO Decoding  Algorithms and VLSI Implementation Aspects"></a>2.2 Christoph Studer - Interative MIMO Decoding  Algorithms and VLSI Implementation Aspects</h2><p><strong>(Studer的博士论文主要关注Channel Decoding与Detection之间通过软信息交换迭代来实现最高准确度的JDD(Joint Detection and Decoding))</strong></p>
<p><strong>主要内容：</strong></p>
<ul>
<li>JDD基本介绍</li>
<li>SISO MMSE PIC<ul>
<li>数学推导</li>
<li>硬件实现及复杂度优化</li>
<li>整体结构模型</li>
<li>VLSI实现结构</li>
</ul>
</li>
<li>SISO Sphere Decoding<ul>
<li>没太看，啥也没懂</li>
</ul>
</li>
<li>SISO Channel Decoding<ul>
<li>LDPC</li>
<li>BCJR</li>
<li>Turbo</li>
</ul>
</li>
</ul>
<h1 id="Part-3-Linear-Detectors"><a href="#Part-3-Linear-Detectors" class="headerlink" title="Part 3 Linear Detectors"></a>Part 3 Linear Detectors</h1><h2 id="3-1-线性迭代近似求逆算法"><a href="#3-1-线性迭代近似求逆算法" class="headerlink" title="3.1 线性迭代近似求逆算法"></a>3.1 线性迭代近似求逆算法</h2><h3 id="3-1-1-Neumann-Series-Expension-proposition-Large-Scale-MIMO-Detection-for-3GPP-LTE-Algorithms-and-FPGA-Implementations"><a href="#3-1-1-Neumann-Series-Expension-proposition-Large-Scale-MIMO-Detection-for-3GPP-LTE-Algorithms-and-FPGA-Implementations" class="headerlink" title="3.1.1 Neumann Series Expension proposition - Large-Scale MIMO Detection for 3GPP LTE: Algorithms and FPGA Implementations"></a>3.1.1 <a href="http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6777306&isnumber=6895322" target="_blank" rel="noopener">Neumann Series Expension proposition - Large-Scale MIMO Detection for 3GPP LTE: Algorithms and FPGA Implementations</a></h3><p><strong>(纽曼级数展开法的提出论文)</strong></p>
<p><strong>主要内容：</strong></p>
<ul>
<li>NS法的数学推导</li>
<li>MATLAB仿真结果</li>
<li>ASIC硬件结构</li>
<li>FPGA实现结果 - 600Mb/s</li>
</ul>
<p><strong>Citation</strong>: M. Wu, B. Yin, G. Wang, C. Dick, J. R. Cavallaro and C. Studer, “Large-Scale MIMO Detection for 3GPP LTE: Algorithms and FPGA Implementations,” in <em>IEEE Journal of Selected Topics in Signal Processing</em>, vol. 8, no. 5, pp. 916-929, Oct. 2014.<br>doi: 10.1109/JSTSP.2014.2313021 </p>
<h3 id="3-1-2-NS-VLSI-A-3-8Gb-s-large-scale-MIMO-detector-for-3GPP-LTE-Advanced"><a href="#3-1-2-NS-VLSI-A-3-8Gb-s-large-scale-MIMO-detector-for-3GPP-LTE-Advanced" class="headerlink" title="3.1.2 NS VLSI - A 3.8Gb/s large-scale MIMO detector for 3GPP LTE-Advanced"></a>3.1.2 <a href="http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6854328&isnumber=6853544" target="_blank" rel="noopener">NS VLSI - A 3.8Gb/s large-scale MIMO detector for 3GPP LTE-Advanced</a></h3><p><strong>(纽曼级数展开法的硬件实现方案，Bei Yin的一篇论文)</strong></p>
<p><strong>Citation:</strong> B. Yin, M. Wu, G. Wang, C. Dick, J. R. Cavallaro and C. Studer, “A 3.8Gb/s large-scale MIMO detector for 3GPP LTE-Advanced,” <em>2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)</em>, Florence, 2014, pp. 3879-3883.<br>doi: 10.1109/ICASSP.2014.6854328 </p>
<h3 id="3-1-3-三对角NS法-On-the-Low-Complexity-Hardware-Friendly-Tridiagonal-Matrix-Inversion-for-Correlated-Massive-MIMO-Systems"><a href="#3-1-3-三对角NS法-On-the-Low-Complexity-Hardware-Friendly-Tridiagonal-Matrix-Inversion-for-Correlated-Massive-MIMO-Systems" class="headerlink" title="3.1.3 三对角NS法 -  On the Low-Complexity, Hardware-Friendly Tridiagonal Matrix Inversion for Correlated Massive MIMO Systems"></a>3.1.3 <a href="http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=8707082&isnumber=8764674" target="_blank" rel="noopener">三对角NS法 -  On the Low-Complexity, Hardware-Friendly Tridiagonal Matrix Inversion for Correlated Massive MIMO Systems</a></h3><p><strong>(东南大学的大佬提出的用三对角阵代替对角阵来进行NS展开法的算法，数学推导很多，而且硬件实现很有创造力)</strong></p>
<p><strong>Citation</strong>: C. Zhang <em>et al</em>., “On the Low-Complexity, Hardware-Friendly Tridiagonal Matrix Inversion for Correlated Massive MIMO Systems,” in <em>IEEE Transactions on Vehicular Technology</em>, vol. 68, no. 7, pp. 6272-6285, July 2019.<br>doi: 10.1109/TVT.2019.2915171 </p>
<h3 id="3-1-4-NI-RI-NS-A-Low-Complexity-Signal-Detection-Scheme-Based-on-Improved-Newton-Iteration-for-Massive-MIMO-Systems"><a href="#3-1-4-NI-RI-NS-A-Low-Complexity-Signal-Detection-Scheme-Based-on-Improved-Newton-Iteration-for-Massive-MIMO-Systems" class="headerlink" title="3.1.4 NI+RI+NS -  A Low Complexity Signal Detection Scheme Based on Improved Newton Iteration for Massive MIMO Systems"></a>3.1.4 <a href="http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=8638827&isnumber=8685247" target="_blank" rel="noopener">NI+RI+NS -  A Low Complexity Signal Detection Scheme Based on Improved Newton Iteration for Massive MIMO Systems</a></h3><p><strong>(牛顿迭代法改进论文，结合了RI和NS)</strong></p>
<p><strong>Citation:</strong> F. Jin, Q. Liu, H. Liu and P. Wu, “A Low Complexity Signal Detection Scheme Based on Improved Newton Iteration for Massive MIMO Systems,” in <em>IEEE Communications Letters</em>, vol. 23, no. 4, pp. 748-751, April 2019.<br>doi: 10.1109/LCOMM.2019.2897798 </p>
<h3 id="3-1-5-Richardson-Iteration-Proposed-Low-Complexity-MMSE-Signal-Detection-Based-on-Richardson-Method-for-Large-Scale-MIMO-Systems"><a href="#3-1-5-Richardson-Iteration-Proposed-Low-Complexity-MMSE-Signal-Detection-Based-on-Richardson-Method-for-Large-Scale-MIMO-Systems" class="headerlink" title="3.1.5 Richardson Iteration Proposed -  Low-Complexity MMSE Signal Detection Based on Richardson Method for Large-Scale MIMO Systems"></a>3.1.5 <a href="http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6966041&isnumber=6965690" target="_blank" rel="noopener">Richardson Iteration Proposed -  Low-Complexity MMSE Signal Detection Based on Richardson Method for Large-Scale MIMO Systems</a></h3><p><strong>(清华老哥写的RI法的提出论文)</strong></p>
<p><strong>Citation</strong>: X. Gao, L. Dai, C. Yuen and Y. Zhang, “Low-Complexity MMSE Signal Detection Based on Richardson Method for Large-Scale MIMO Systems,” <em>2014 IEEE 80th Vehicular Technology Conference (VTC2014-Fall)</em>, Vancouver, BC, 2014, pp. 1-5.<br>doi: 10.1109/VTCFall.2014.6966041 </p>
<p><strong>注：</strong>清华老哥在写这篇会议的时候还投了一篇letter，内容是基本一样的，letter的内容更少一点。 </p>
<p>X. Gao, L. Dai, Y. Ma and Z. Wang, “Low-complexity near-optimal signal detection for uplink large-scale MIMO systems,” in <em>Electronics Letters</em>, vol. 50, no. 18, pp. 1326-1328, 28 August 2014.<br>doi: 10.1049/el.2014.0713 </p>
<h3 id="3-1-6-CG-VLSI-VLSI-design-of-large-scale-soft-output-MIMO-detection-using-conjugate-gradients"><a href="#3-1-6-CG-VLSI-VLSI-design-of-large-scale-soft-output-MIMO-detection-using-conjugate-gradients" class="headerlink" title="3.1.6 CG VLSI - VLSI design of large-scale soft-output MIMO detection using conjugate gradients"></a>3.1.6 <a href="http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=7168929&isnumber=7168553" target="_blank" rel="noopener">CG VLSI - VLSI design of large-scale soft-output MIMO detection using conjugate gradients</a></h3><p><strong>(B.Yin的CG法及CGLS的硬件实现，内容基本包含在了他的博士论文里面，还不如博士论文里面的全面)</strong></p>
<p><strong>Citation</strong>: B. Yin, M. Wu, J. R. Cavallaro and C. Studer, “VLSI design of large-scale soft-output MIMO detection using conjugate gradients,” <em>2015 IEEE International Symposium on Circuits and Systems (ISCAS)</em>, Lisbon, 2015, pp. 1498-1501.<br>doi: 10.1109/ISCAS.2015.7168929 </p>
<h3 id="3-1-7-PCI-Low-Computing-Load-High-Parallelism-Detection-Method-Based-on-Chebyshev-Iteration-for-Massive-MIMO-Systems-With-VLSI-Architecture"><a href="#3-1-7-PCI-Low-Computing-Load-High-Parallelism-Detection-Method-Based-on-Chebyshev-Iteration-for-Massive-MIMO-Systems-With-VLSI-Architecture" class="headerlink" title="3.1.7 PCI - Low-Computing-Load, High-Parallelism Detection Method Based on Chebyshev Iteration for Massive MIMO Systems With VLSI Architecture"></a>3.1.7 <a href="http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=7912331&isnumber=7924436" target="_blank" rel="noopener">PCI - Low-Computing-Load, High-Parallelism Detection Method Based on Chebyshev Iteration for Massive MIMO Systems With VLSI Architecture</a></h3><p><strong>(清华老哥提出的并行切比雪夫迭代法)</strong></p>
<p><strong>Citation</strong>: G. Peng, L. Liu, P. Zhang, S. Yin and S. Wei, “Low-Computing-Load, High-Parallelism Detection Method Based on Chebyshev Iteration for Massive MIMO Systems With VLSI Architecture,” in <em>IEEE Transactions on Signal Processing</em>, vol. 65, no. 14, pp. 3775-3788, 15 July15, 2017.<br>doi: 10.1109/TSP.2017.2698410 </p>
<h3 id="3-1-8-GS-Proposition-Low-Complexity-Soft-Output-Signal-Detection-Based-on-Gauss–Seidel-Method-for-Uplink-Multiuser-Large-Scale-MIMO-Systems"><a href="#3-1-8-GS-Proposition-Low-Complexity-Soft-Output-Signal-Detection-Based-on-Gauss–Seidel-Method-for-Uplink-Multiuser-Large-Scale-MIMO-Systems" class="headerlink" title="3.1.8 GS Proposition - Low-Complexity Soft-Output Signal Detection Based on Gauss–Seidel Method for Uplink Multiuser Large-Scale MIMO Systems"></a>3.1.8 <a href="http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6954512&isnumber=7297784" target="_blank" rel="noopener">GS Proposition - Low-Complexity Soft-Output Signal Detection Based on Gauss–Seidel Method for Uplink Multiuser Large-Scale MIMO Systems</a></h3><p><strong>(GS - Gauss-Seidel迭代法的提出论文，性能非常优越的迭代法)</strong></p>
<p><strong>Citation</strong>: L. Dai, X. Gao, X. Su, S. Han, C. I and Z. Wang, “Low-Complexity Soft-Output Signal Detection Based on Gauss–Seidel Method for Uplink Multiuser Large-Scale MIMO Systems,” in <em>IEEE Transactions on Vehicular Technology</em>, vol. 64, no. 10, pp. 4839-4845, Oct. 2015.<br>doi: 10.1109/TVT.2014.2370106 </p>
<h3 id="3-1-9-GS-VLSI-Efficient-architecture-for-soft-output-massive-MIMO-detection-with-Gauss-Seidel-method"><a href="#3-1-9-GS-VLSI-Efficient-architecture-for-soft-output-massive-MIMO-detection-with-Gauss-Seidel-method" class="headerlink" title="3.1.9 GS VLSI - Efficient architecture for soft-output massive MIMO detection with Gauss-Seidel method"></a>3.1.9 <a href="http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=7538940&isnumber=7527154" target="_blank" rel="noopener">GS VLSI - Efficient architecture for soft-output massive MIMO detection with Gauss-Seidel method</a></h3><p><strong>(GS 的VLSI设计论文，其中放出了FPGA的实现结果，但是并没有流片结果)</strong></p>
<p><strong>Citation</strong>:  Z. Wu, C. Zhang, Y. Xue, S. Xu and X. You, “Efficient architecture for soft-output massive MIMO detection with Gauss-Seidel method,” <em>2016 IEEE International Symposium on Circuits and Systems (ISCAS)</em>, Montreal, QC, 2016, pp. 1886-1889.<br>doi: 10.1109/ISCAS.2016.7538940 </p>
<h3 id="3-1-10-Jacobi-联合迭代-A-Near-Optimal-Detection-Scheme-Based-on-Joint-Steepest-Descent-and-Jacobi-Method-for-Uplink-Massive-MIMO-Systems"><a href="#3-1-10-Jacobi-联合迭代-A-Near-Optimal-Detection-Scheme-Based-on-Joint-Steepest-Descent-and-Jacobi-Method-for-Uplink-Massive-MIMO-Systems" class="headerlink" title="3.1.10 Jacobi 联合迭代 - A Near-Optimal Detection Scheme Based on Joint Steepest Descent and Jacobi Method for Uplink Massive MIMO Systems"></a>3.1.10 <a href="http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=7342925&isnumber=7399440" target="_blank" rel="noopener">Jacobi 联合迭代 - A Near-Optimal Detection Scheme Based on Joint Steepest Descent and Jacobi Method for Uplink Massive MIMO Systems</a></h3><p><strong>(秦晓波学长的论文，主要思想为Jacobi的联合迭代法，可参考的地方在于其在最后有列算法复杂度和FPGA实现结果的比较，很多算法都有包括)</strong></p>
<p><strong>算法复杂度和FPGA实现结果包含算法：</strong></p>
<ul>
<li>算法复杂度：<ul>
<li>NS</li>
<li>RI</li>
<li>CG</li>
<li>GS</li>
<li>SD</li>
<li>JC</li>
</ul>
</li>
<li>FPGA实现结果：<ul>
<li>Cholesky</li>
<li>NS</li>
<li>RI</li>
<li>CG</li>
<li>GS</li>
</ul>
</li>
</ul>
<h2 id="3-2-线性算法Asic-Implementation-论文"><a href="#3-2-线性算法Asic-Implementation-论文" class="headerlink" title="3.2 线性算法Asic Implementation 论文"></a>3.2 线性算法Asic Implementation 论文</h2><h3 id="3-2-1-清华彭桂强TCAS-1-1-58-Gbps-W-0-40-Gbps-mm2-ASIC-Implementation-of-MMSE-Detection-for-128-times-8-64-QAM-Massive-MIMO-in-65-nm-CMOS"><a href="#3-2-1-清华彭桂强TCAS-1-1-58-Gbps-W-0-40-Gbps-mm2-ASIC-Implementation-of-MMSE-Detection-for-128-times-8-64-QAM-Massive-MIMO-in-65-nm-CMOS" class="headerlink" title="3.2.1 清华彭桂强TCAS-1 -  1.58 Gbps/W 0.40 Gbps/mm2 ASIC Implementation of MMSE Detection for $128\times 8~64$ -QAM Massive MIMO in 65 nm CMOS"></a>3.2.1 <a href="https://ieeexplore.ieee.org/document/8051120" target="_blank" rel="noopener">清华彭桂强TCAS-1 -  1.58 Gbps/W 0.40 Gbps/mm2 ASIC Implementation of MMSE Detection for $128\times 8~64$ -QAM Massive MIMO in 65 nm CMOS</a></h3><p><strong>Citation</strong>: G. Peng, L. Liu, S. Zhou, S. Yin and S. Wei, “A 1.58 Gbps/W 0.40 Gbps/mm2 ASIC Implementation of MMSE Detection for $128\times 8~64$ -QAM Massive MIMO in 65 nm CMOS,” in <em>IEEE Transactions on Circuits and Systems I: Regular Papers</em>, vol. 65, no. 5, pp. 1717-1730, May 2018.<br>doi: 10.1109/TCSI.2017.2754282</p>
<p><strong>清华彭桂强老哥的东西，算法上的创新很少，硬件设计也没有特别出彩，但是有流片（实验室有钱），所以还是得尊敬一波。</strong></p>
<p><strong>这篇其实可以作为硬件入门的初级论文，非常详细的讲了Gram矩阵求解和迭代流水线结构，清晰明了，值得学习。</strong></p>
<h3 id="3-2-2-东南大学张川的GS硬件，创新点一般，写的也一般-Efficient-Soft-Output-Gauss-Seidel-Data-Detector-for-Massive-MIMO-Systems"><a href="#3-2-2-东南大学张川的GS硬件，创新点一般，写的也一般-Efficient-Soft-Output-Gauss-Seidel-Data-Detector-for-Massive-MIMO-Systems" class="headerlink" title="3.2.2 东南大学张川的GS硬件，创新点一般，写的也一般 - Efficient Soft-Output Gauss-Seidel Data Detector for Massive MIMO Systems"></a>3.2.2 <a href="https://ieeexplore.ieee.org/document/8511052" target="_blank" rel="noopener">东南大学张川的GS硬件，创新点一般，写的也一般 - Efficient Soft-Output Gauss-Seidel Data Detector for Massive MIMO Systems</a></h3><p><strong>Citation</strong>: C. Zhang, Z. Wu, C. Studer, Z. Zhang and X. You, “Efficient Soft-Output Gauss-Seidel Data Detector for Massive MIMO Systems,” in <em>IEEE Transactions on Circuits and Systems I: Regular Papers</em>.<br>doi: 10.1109/TCSI.2018.2875741</p>
<h1 id="Part-4-Non-linear-Detectors"><a href="#Part-4-Non-linear-Detectors" class="headerlink" title="Part 4 Non-linear Detectors"></a>Part 4 Non-linear Detectors</h1><h2 id="4-1-Lattice-Reduction"><a href="#4-1-Lattice-Reduction" class="headerlink" title="4.1 Lattice Reduction"></a>4.1 Lattice Reduction</h2><h3 id="4-1-1-ELR-Element-Based-Lattice-Reduction-Algorithms-for-Large-MIMO-Detection"><a href="#4-1-1-ELR-Element-Based-Lattice-Reduction-Algorithms-for-Large-MIMO-Detection" class="headerlink" title="4.1.1 ELR - Element-Based Lattice Reduction Algorithms for Large MIMO Detection"></a>4.1.1 <a href="https://ieeexplore.ieee.org/document/6415398" target="_blank" rel="noopener">ELR - Element-Based Lattice Reduction Algorithms for Large MIMO Detection</a></h3><p><strong>Citation</strong>: Q. Zhou and X. Ma, “Element-Based Lattice Reduction Algorithms for Large MIMO Detection,” in <em>IEEE Journal on Selected Areas in Communications</em>, vol. 31, no. 2, pp. 274-286, February 2013.<br>doi: 10.1109/JSAC.2013.130215</p>
<p><strong>佐治亚理工的马晓丽团队2013年的LR系列的算法 - ELR，主要阐明了一种新的格基规约算法，基于Dual-lattice的规约方法。</strong></p>
<p><strong>主要作用于$C=(H^{H}H)^{-1}$对角线元素的约减，根据不同的约减迭代结束条件，分为D-ELR-SLV和D-ELR-SLB两种算法。</strong></p>
<h3 id="4-1-2-Improved-ELR-Improved-Element-Based-Lattice-Reduction-Algorithms-for-Wireless-Communications"><a href="#4-1-2-Improved-ELR-Improved-Element-Based-Lattice-Reduction-Algorithms-for-Wireless-Communications" class="headerlink" title="4.1.2 Improved ELR - Improved Element-Based Lattice Reduction Algorithms for Wireless Communications"></a>4.1.2 <a href="https://ieeexplore.ieee.org/document/6575077" target="_blank" rel="noopener">Improved ELR - Improved Element-Based Lattice Reduction Algorithms for Wireless Communications</a></h3><p><strong>Citation</strong>: Q. Zhou and X. Ma, “Improved Element-Based Lattice Reduction Algorithms for Wireless Communications,” in <em>IEEE Transactions on Wireless Communications</em>, vol. 12, no. 9, pp. 4414-4421, September 2013.<br>doi: 10.1109/TWC.2013.072513.121479</p>
<p><strong>佐治亚理工马晓丽团队2013年接续4.1.1的JSAC发表在TWC上面的改进论文，主要是改进ELR的遍历和规约方式。</strong></p>
<p><strong>改进主要体现在，每次基向量更新不再是只更新最大值列和行了，而是将整个矩阵进行更新，这样复杂度成倍增加，当然性能会优异很多。</strong></p>
<h3 id="4-1-3-FDLR-A-Low-Complexity-MIMO-Detector-Based-on-Fast-Dual-Lattice-Reduction-Algorithm"><a href="#4-1-3-FDLR-A-Low-Complexity-MIMO-Detector-Based-on-Fast-Dual-Lattice-Reduction-Algorithm" class="headerlink" title="4.1.3 FDLR - A Low-Complexity MIMO Detector Based on Fast Dual-Lattice Reduction Algorithm"></a>4.1.3 <a href="https://ieeexplore.ieee.org/document/7880859" target="_blank" rel="noopener">FDLR - A Low-Complexity MIMO Detector Based on Fast Dual-Lattice Reduction Algorithm</a></h3><p><strong>Citation</strong>: C. Jing, X. Wang, B. Chen, Y. Ma and J. Wei, “A Low-Complexity MIMO Detector Based on Fast Dual-Lattice Reduction Algorithm,” <em>2016 IEEE 84th Vehicular Technology Conference (VTC-Fall)</em>, Montreal, QC, 2016, pp. 1-6.<br>doi: 10.1109/VTCFall.2016.7880859</p>
<p><strong>国防科大的老哥提出的格基规约算法 - FDLR快速格基规约算法，同样也是作用于Dual-lattice域</strong></p>
<p><strong>这篇文章的思路与4.1.1蛮类似的，但是存在着计算$\lambda_{i,j}= \lfloor \frac{b_{j}^{H}b_{i}}{|| b_{j} ||^{2}} \rceil$ 和类似正交分离度的计算，计算复杂度过高</strong></p>
<h3 id="4-1-4-LR综述类Magazine-Lattice-Reduction"><a href="#4-1-4-LR综述类Magazine-Lattice-Reduction" class="headerlink" title="4.1.4 LR综述类Magazine - Lattice Reduction"></a>4.1.4 <a href="https://ieeexplore.ieee.org/document/5753113" target="_blank" rel="noopener">LR综述类Magazine - Lattice Reduction</a></h3><p><strong>Citation</strong>: D. Wübben, D. Seethaler, J. Jaldén and G. Matz, “Lattice Reduction,” in <em>IEEE Signal Processing Magazine</em>, vol. 28, no. 3, pp. 70-91, May 2011.<br>doi: 10.1109/MSP.2010.938758</p>
<p><strong>这是我LR入门看的文献，2011年的Magazine，比较通俗的讲述了LR的基本知识，包含了Dual-lattice域的知识，是非常好的入门教材</strong></p>

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                <ul class="menu-list"><li>
        <a class="is-flex" href="#Part-1-Survey-amp-Tutorial">
        <!-- <span class="has-mr-6">1</span> -->
        <span>Part 1 Survey &amp; Tutorial</span>
        </a><ul class="menu-list"><li>
        <a class="is-flex" href="#1-1Massive-MIMO-Detection-Techniques-A-Survey">
        <!-- <span class="has-mr-6">1.1</span> -->
        <span>1.1Massive MIMO Detection Techniques: A Survey</span>
        </a></li><li>
        <a class="is-flex" href="#1-2-Massive-MIMO-An-Introduction">
        <!-- <span class="has-mr-6">1.2</span> -->
        <span>1.2 Massive MIMO: An Introduction</span>
        </a></li><li>
        <a class="is-flex" href="#1-3-Fifty-Years-of-MIMO-Detection-The-Road-to-Large-Scale-MIMOs">
        <!-- <span class="has-mr-6">1.3</span> -->
        <span>1.3 Fifty Years of MIMO Detection: The Road to Large-Scale MIMOs</span>
        </a></li></ul></li><li>
        <a class="is-flex" href="#Part-2-Dissertation-Doctoral-or-Master’s">
        <!-- <span class="has-mr-6">2</span> -->
        <span>Part 2 Dissertation (Doctoral or Master’s)</span>
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        <a class="is-flex" href="#2-1-Bei-Yin-Low-Complexity-Detection-and-Precoding-for-Massive-MIMO-Systems-Algorithm-Architectures-and-Application">
        <!-- <span class="has-mr-6">2.1</span> -->
        <span>2.1 Bei Yin - Low Complexity Detection and Precoding for Massive MIMO Systems: Algorithm, Architectures, and Application</span>
        </a></li><li>
        <a class="is-flex" href="#2-2-Christoph-Studer-Interative-MIMO-Decoding-Algorithms-and-VLSI-Implementation-Aspects">
        <!-- <span class="has-mr-6">2.2</span> -->
        <span>2.2 Christoph Studer - Interative MIMO Decoding  Algorithms and VLSI Implementation Aspects</span>
        </a></li></ul></li><li>
        <a class="is-flex" href="#Part-3-Linear-Detectors">
        <!-- <span class="has-mr-6">3</span> -->
        <span>Part 3 Linear Detectors</span>
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        <a class="is-flex" href="#3-1-线性迭代近似求逆算法">
        <!-- <span class="has-mr-6">3.1</span> -->
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        <a class="is-flex" href="#3-1-1-Neumann-Series-Expension-proposition-Large-Scale-MIMO-Detection-for-3GPP-LTE-Algorithms-and-FPGA-Implementations">
        <!-- <span class="has-mr-6">3.1.1</span> -->
        <span>3.1.1 Neumann Series Expension proposition - Large-Scale MIMO Detection for 3GPP LTE: Algorithms and FPGA Implementations</span>
        </a></li><li>
        <a class="is-flex" href="#3-1-2-NS-VLSI-A-3-8Gb-s-large-scale-MIMO-detector-for-3GPP-LTE-Advanced">
        <!-- <span class="has-mr-6">3.1.2</span> -->
        <span>3.1.2 NS VLSI - A 3.8Gb/s large-scale MIMO detector for 3GPP LTE-Advanced</span>
        </a></li><li>
        <a class="is-flex" href="#3-1-3-三对角NS法-On-the-Low-Complexity-Hardware-Friendly-Tridiagonal-Matrix-Inversion-for-Correlated-Massive-MIMO-Systems">
        <!-- <span class="has-mr-6">3.1.3</span> -->
        <span>3.1.3 三对角NS法 -  On the Low-Complexity, Hardware-Friendly Tridiagonal Matrix Inversion for Correlated Massive MIMO Systems</span>
        </a></li><li>
        <a class="is-flex" href="#3-1-4-NI-RI-NS-A-Low-Complexity-Signal-Detection-Scheme-Based-on-Improved-Newton-Iteration-for-Massive-MIMO-Systems">
        <!-- <span class="has-mr-6">3.1.4</span> -->
        <span>3.1.4 NI+RI+NS -  A Low Complexity Signal Detection Scheme Based on Improved Newton Iteration for Massive MIMO Systems</span>
        </a></li><li>
        <a class="is-flex" href="#3-1-5-Richardson-Iteration-Proposed-Low-Complexity-MMSE-Signal-Detection-Based-on-Richardson-Method-for-Large-Scale-MIMO-Systems">
        <!-- <span class="has-mr-6">3.1.5</span> -->
        <span>3.1.5 Richardson Iteration Proposed -  Low-Complexity MMSE Signal Detection Based on Richardson Method for Large-Scale MIMO Systems</span>
        </a></li><li>
        <a class="is-flex" href="#3-1-6-CG-VLSI-VLSI-design-of-large-scale-soft-output-MIMO-detection-using-conjugate-gradients">
        <!-- <span class="has-mr-6">3.1.6</span> -->
        <span>3.1.6 CG VLSI - VLSI design of large-scale soft-output MIMO detection using conjugate gradients</span>
        </a></li><li>
        <a class="is-flex" href="#3-1-7-PCI-Low-Computing-Load-High-Parallelism-Detection-Method-Based-on-Chebyshev-Iteration-for-Massive-MIMO-Systems-With-VLSI-Architecture">
        <!-- <span class="has-mr-6">3.1.7</span> -->
        <span>3.1.7 PCI - Low-Computing-Load, High-Parallelism Detection Method Based on Chebyshev Iteration for Massive MIMO Systems With VLSI Architecture</span>
        </a></li><li>
        <a class="is-flex" href="#3-1-8-GS-Proposition-Low-Complexity-Soft-Output-Signal-Detection-Based-on-Gauss–Seidel-Method-for-Uplink-Multiuser-Large-Scale-MIMO-Systems">
        <!-- <span class="has-mr-6">3.1.8</span> -->
        <span>3.1.8 GS Proposition - Low-Complexity Soft-Output Signal Detection Based on Gauss–Seidel Method for Uplink Multiuser Large-Scale MIMO Systems</span>
        </a></li><li>
        <a class="is-flex" href="#3-1-9-GS-VLSI-Efficient-architecture-for-soft-output-massive-MIMO-detection-with-Gauss-Seidel-method">
        <!-- <span class="has-mr-6">3.1.9</span> -->
        <span>3.1.9 GS VLSI - Efficient architecture for soft-output massive MIMO detection with Gauss-Seidel method</span>
        </a></li><li>
        <a class="is-flex" href="#3-1-10-Jacobi-联合迭代-A-Near-Optimal-Detection-Scheme-Based-on-Joint-Steepest-Descent-and-Jacobi-Method-for-Uplink-Massive-MIMO-Systems">
        <!-- <span class="has-mr-6">3.1.10</span> -->
        <span>3.1.10 Jacobi 联合迭代 - A Near-Optimal Detection Scheme Based on Joint Steepest Descent and Jacobi Method for Uplink Massive MIMO Systems</span>
        </a></li></ul></li><li>
        <a class="is-flex" href="#3-2-线性算法Asic-Implementation-论文">
        <!-- <span class="has-mr-6">3.2</span> -->
        <span>3.2 线性算法Asic Implementation 论文</span>
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        <a class="is-flex" href="#3-2-1-清华彭桂强TCAS-1-1-58-Gbps-W-0-40-Gbps-mm2-ASIC-Implementation-of-MMSE-Detection-for-128-times-8-64-QAM-Massive-MIMO-in-65-nm-CMOS">
        <!-- <span class="has-mr-6">3.2.1</span> -->
        <span>3.2.1 清华彭桂强TCAS-1 -  1.58 Gbps/W 0.40 Gbps/mm2 ASIC Implementation of MMSE Detection for $128\times 8~64$ -QAM Massive MIMO in 65 nm CMOS</span>
        </a></li><li>
        <a class="is-flex" href="#3-2-2-东南大学张川的GS硬件，创新点一般，写的也一般-Efficient-Soft-Output-Gauss-Seidel-Data-Detector-for-Massive-MIMO-Systems">
        <!-- <span class="has-mr-6">3.2.2</span> -->
        <span>3.2.2 东南大学张川的GS硬件，创新点一般，写的也一般 - Efficient Soft-Output Gauss-Seidel Data Detector for Massive MIMO Systems</span>
        </a></li></ul></li></ul></li><li>
        <a class="is-flex" href="#Part-4-Non-linear-Detectors">
        <!-- <span class="has-mr-6">4</span> -->
        <span>Part 4 Non-linear Detectors</span>
        </a><ul class="menu-list"><li>
        <a class="is-flex" href="#4-1-Lattice-Reduction">
        <!-- <span class="has-mr-6">4.1</span> -->
        <span>4.1 Lattice Reduction</span>
        </a><ul class="menu-list"><li>
        <a class="is-flex" href="#4-1-1-ELR-Element-Based-Lattice-Reduction-Algorithms-for-Large-MIMO-Detection">
        <!-- <span class="has-mr-6">4.1.1</span> -->
        <span>4.1.1 ELR - Element-Based Lattice Reduction Algorithms for Large MIMO Detection</span>
        </a></li><li>
        <a class="is-flex" href="#4-1-2-Improved-ELR-Improved-Element-Based-Lattice-Reduction-Algorithms-for-Wireless-Communications">
        <!-- <span class="has-mr-6">4.1.2</span> -->
        <span>4.1.2 Improved ELR - Improved Element-Based Lattice Reduction Algorithms for Wireless Communications</span>
        </a></li><li>
        <a class="is-flex" href="#4-1-3-FDLR-A-Low-Complexity-MIMO-Detector-Based-on-Fast-Dual-Lattice-Reduction-Algorithm">
        <!-- <span class="has-mr-6">4.1.3</span> -->
        <span>4.1.3 FDLR - A Low-Complexity MIMO Detector Based on Fast Dual-Lattice Reduction Algorithm</span>
        </a></li><li>
        <a class="is-flex" href="#4-1-4-LR综述类Magazine-Lattice-Reduction">
        <!-- <span class="has-mr-6">4.1.4</span> -->
        <span>4.1.4 LR综述类Magazine - Lattice Reduction</span>
        </a></li></ul></li></ul></li></ul>
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